1. Field of the Invention
The present invention relates to analysis of neuronal activities in neuronal areas, for example of nerve structures in areas of the brain of a patient.
2. Description of the Prior Art
Knowledge about a mode of operation of a neuronal area and about an interaction of neuronal areas are fundamental to functional magnetic resonance tomography (fMRI), as described in A. W. Toga and J. C. Maziotta (Ed.), “Brain Mapping: The Methods”, Ch 9: M. S. Cohen: “Rapid MRI and Functional Applications”, Academic Press 1996, which is a further development of magnetic resonance tomography.
Magnetic resonance tomography is an imaging method that produces sectional images of the human body without using damaging X-rays.
Instead MR takes advantage of the behavior of body tissue in a strong magnetic field. Pathological changes in body tissue, for example in the brain or spinal cord, can be detected by this modality.
Functional disorders in body tissue, particularly in the brain of a patient, however, cannot be detected by means of conventional magnetic resonance tomography.
This is performed by functional magnetic resonance tomography or fMRI technology.
Neuronal activity in areas of the brain of a patient can be measured indirectly by means of the fMRI technique. The BOLD (Blood Oxygenation Level Dependent) signal, as it is called, is measured in individual areas of the brain, this signal relating to neuronal activity in the respective areas.
Dependencies, which stem among other things from structures in the brain, i.e. from neuronal links between nerve cells or nerve structures, exist between the neuronal activities in the areas.
The outcome of the fMRI measurements shows the course of activity of individual areas over a certain period, for example during cognitive sequences as a result of specific perception processes or motor tasks.
Functional disorders, in this case in the brain, are thus inherently contained in the fMRI signals measured.
Efficient methods for the analysis and evaluation of such fMRI measurements are desirable in order to be able to furnish evidence of possibly existing functional disorders in specific areas.
Known methods, such as described in A. R. McIntosh et al., Structural Equation Modeling and Its Application to Network Analysis in Functional Brain Imaging, Human Brain Mapping, 2:2-22, 1994, are restricted to detection of functional relationships between various areas of the brain in certain predetermined tasks such as the aforementioned perception processes or motor tasks (functional connectivity). These functional relationships are also designated functional connectivity.
In contrast to functional connectivity, however, the determination of a true physical connectivity, i.e. the determination of actually existing linking structures (of areas of the brain) independently of specific predetermined tasks, is not possible with these known methods.
A further known method of analysis for detecting functional connectivity is described below.
The object of this known method of analysis described below is the above-described detection of functional relationships between various areas of the brain in specific perception processes or motor tasks.
This known method of analysis is based on a predefined model of a brain, i.e. a predefined brain architecture.
This brain architecture, predetermined from prior knowledge, defines general functional and/or spatial dependencies between specific areas of the brain in the form of a coupling matrix S, as it is called.
The coupling matrix S has a form or structure that is fixed in accordance with the predetermined brain architecture (columns/rows) and is accordingly populated in certain, but not at all (matrix) positions, with changeable coupling strengths Si. These are changeable and are matched as part of the method of analysis.
The unpopulated (matrix) positions are populated with fixed, unchangeable values, namely zero.
The coupling strengths Si describe functional dependencies respectively between two areas of the brain or the BOLD signals measured there and represent the neuronal activities there.
In this known method of analysis, the (changeable) coupling strengths Si are defined such that statistical characteristic quantities that are determined by this method of analysis from the fMRI measurements, can best be explained. Expressed differently, the probability for an occurrence of the measured data, i.e. the fMRI measurement or the BOLD signals, is maximized by means of the desired coupling strengths Si.
In this method of analysis a data point s=st represents a totality of all BOLD signals s1, . . . , sN of the individual n areas at a point in time t or averaged over a time interval t (t=[1;T]).
The fMRI measurement includes a large number of such data points for possibly differing perception processes and/or motor tasks, for which the corresponding BOLD signals were measured.
In this known method of analysis, it is not the individual data points s1, s2, . . . , St, which are evaluated directly, but statistical characteristic quantities that emerge from these.
For a statistical distribution of the data points s1, s2, . . . , sT it is assumed that it is described fully by a multivariant normal distribution, i.e. a statistical distribution of the first order, with a mean value m and a covariance Σ:
                              P          ⁡                      (                                          s                ❘                μ                            ,              Σ                        )                          =                              1                                                                                2                    ⁢                    π                                                  N                            ·                                              Σ                                                              ·                      ⅇ                                          -                                  1                  2                                            ⁢                                                (                                      s                    -                    μ                                    )                                ′                            ⁢                                                ∑                                      -                    1                                                  ⁢                                  (                                      s                    -                    μ                                    )                                                                                        (        1        )            
For sufficiently long series of measurements, the occurrence of the individual data points si of s1, s2, . . . , sT can be viewed as statistically independent.
The probability P=P(s1, . . . , sT|μ, Σ) for an occurrence of all measured data points s1, . . . , sT can accordingly be written as:
                              P          ⁡                      (                                          s                1                            ,              …              ⁢                                                          ,                                                s                  T                                ❘                μ                            ,              Σ                        )                          =                                            ∏                              t                =                1                            T                        ⁢                          P              ⁡                              (                                                                            s                      t                                        ❘                    μ                                    ,                  Σ                                )                                              =                                          ⁢                                    1                                                                                          2                      ⁢                      π                                                        NT                                ·                                                                          Σ                                                        T                                                      ·                          ⅇ                                                -                                      1                    2                                                  ⁢                                                      ∑                                          t                      =                      1                                        T                                    ⁢                                                                                    (                                                                              s                            t                                                    -                          μ                                                )                                            ′                                        ⁢                                                                  ∑                                                  -                          1                                                                    ⁢                                              (                                                                              s                            t                                                    -                          μ                                                )                                                                                                                                                    (        2        )            
Here, the unknown variables, the mean value μ and the covariance Σ, depend exclusively on a(brain) model that describes the measured data.
The model assumes a linear statistical relationship between the individual BOLD signals:
                                                        s              i                        =                                                                                ∑                                          j                      =                      1                                        N                                    ⁢                                                            S                      ij                                        ⁢                                          s                      j                                                                      +                                                      ɛ                    i                                    ⁢                                                                          ⁢                  for                  ⁢                                                                          ⁢                  i                                            =              1                                ,          …          ⁢                                          ,          N                ⁢                                  ⁢        or        ⁢                                  ⁢                  s          =                      Ss            +            ɛ                                              (        3        )            where ε designates the external influence on the individual BOLD signals, like a sensory input of sensory cells on the examined areas of the brain.
The influence variables εi and εj on different examined areas i and j can in this case be correlated throughout.
The model parameters to be specified are consequently the coupling strengths Si of the underlying coupling matrix S, the mean value με of the external influence ε and the covariance Σε of ε.
The mean value μ and the covariance Σ depend on these:μ=μ(S,με)Σ=Σ(S, Σε)  (4)
In this known method of analysis the model parameters are then determined such that the probability P=P(s1, . . . , sT|μ,Σ) given in (2) for the occurrence of the measured data is maximized.
For this purpose, a known maximum likelihood estimation method (optimization) is applied such as described in T. W. Anderson, An Introduction to Multivariable Statistical Analysis, Chapter 3, John Wiley & Sons, Inc., New York, London, Sydney, 1994.
Using the relationships (4) in (2), an expression that is dependent on the coupling strengths Si, the mean value με and the covariance Σε is obtained, which expression is maximized by the optimization.
The optimization then leads to the desired coupling strengths Si between the BOLD signals.
These in turn enable detection of functional relationships between various areas of the brain in specific perception processes or motor tasks (functional connectivity).
This known method of analysis exhibits the disadvantage that the measured fMRI signals are able to be modeled only insufficiently accurately or that the model is matchable only insufficiently accurately to the measured fMRI signals, and consequently the mode of operation or interaction of neuronal areas is only insufficiently mappable. This shortcoming could possibly lead to incorrect conclusions being made with regard to connective functionality.
A software tool for fMRI analysis, an “fmri.pro”, is known from Specification for “fmri.pro” software relating to quantitative fMRI analysis, obtainable on Jul. 9, 2001, under http://www.med.uni-uenchen.de/radin/html/arbeitsgruppen/fmri/ccfmri.html. A device for implementing the fMRI technique is known from Specification of fMRI—device, obtainable on Jul. 9, 2001, under http://www.unipublic.unizh.ch/campus/uninews/2001/0147/fmri.html.